Although the Cox proportional hazards model is well established and extensively used in the analysis of survival data, the proportional hazards (PH) assumption may not always hold in practical scenarios. The semiparametric transformation model extends the conventional Cox model and also includes many other survival models as special cases. This paper introduces a deep partially linear transformation model (DPLTM) as a general and flexible framework for estimation, inference and prediction. The proposed method is capable of avoiding the curse of dimensionality while still retaining the interpretability of some covariates of interest. We derive the overall convergence rate of the maximum likelihood estimators, the minimax lower bound of the nonparametric deep neural network (DNN) estimator, the asymptotic normality and the semiparametric efficiency of the parametric estimator. Comprehensive simulation studies demonstrate the impressive performance of the proposed estimation procedure in terms of both estimation accuracy and prediction power, which is further validated by an application to a real-world dataset.

翻译：尽管Cox比例风险模型在生存数据分析中已得到广泛确立和应用，但在实际场景中比例风险（PH）假设可能并不总是成立。半参数变换模型扩展了传统的Cox模型，并将许多其他生存模型作为特例包含其中。本文提出了一种深度部分线性变换模型（DPLTM），作为估计、推断和预测的通用灵活框架。该方法能够在避免维度灾难的同时，保留部分感兴趣协变量的可解释性。我们推导了最大似然估计量的整体收敛速率、非参数深度神经网络（DNN）估计量的极小极大下界、参数估计量的渐近正态性以及半参数有效性。综合模拟研究表明，所提出的估计方法在估计精度和预测能力方面均表现出卓越性能，这一结论通过对真实世界数据集的应用得到了进一步验证。